#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
vector<vector<pair<int, int>>> CalcSegments(const vector<int>& a) {
int n = static_cast<int>(a.size());
vector<vector<pair<int, int>>> segments(n);
vector<int> s;
for (int i = 0; i < n; ++i) {
while (!s.empty()) {
int segment = i - s.back() - 1;
if (segment > 0)
segments[i].emplace_back(segment, 1);
if (a[s.back()] >= a[i])
break;
s.pop_back();
}
if (!s.empty() && a[s.back()] == a[i])
s.pop_back();
s.push_back(i);
}
segments.shrink_to_fit();
return segments;
}
vector<pair<int, int>> Merge(const vector<pair<int, int>>& a, const vector<pair<int, int>>& b) {
vector<pair<int, int>> r;
int a_size = static_cast<int>(a.size());
int j = 0;
for (const auto& e: b) {
while (j < a_size && a[j].first < e.first) {
++j;
}
int cnt = e.second;
if (j < a_size && a[j].first == e.first) {
cnt += a[j].second;
}
r.emplace_back(e.first, cnt);
}
return r;
}
long long count_rectangles(std::vector<std::vector<int> > a) {
int n = static_cast<int>(a.size());
int m = static_cast<int>(a.front().size());
vector<vector<vector<pair<int, int>>>> horizontal_segments(n, vector<vector<pair<int, int>>>(m));
vector<vector<vector<pair<int, int>>>> vertical_segments(n, vector<vector<pair<int, int>>>(m));
for (int i = 0; i < n; ++i) {
horizontal_segments[i] = CalcSegments(a[i]);
}
for (int j = 0; j < m; ++j) {
vector<int> b;
for (int i = 0; i < n; ++i) {
b.push_back(a[i][j]);
}
auto segments = CalcSegments(b);
for (int i = 0; i < n; ++i) {
vertical_segments[i][j] = segments[i];
}
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
if (i > 0) horizontal_segments[i][j] = Merge(horizontal_segments[i - 1][j], horizontal_segments[i][j]);
if (j > 0) vertical_segments[i][j] = Merge(vertical_segments[i][j - 1], vertical_segments[i][j]);
}
}
long long result = 0;
for (int i = 1; i < n; ++i) {
for (int j = 0; j < m; ++j) {
for (auto& x: horizontal_segments[i - 1][j]) {
for (auto& y: vertical_segments[i][j - 1]) {
if (x.first <= y.second && y.first <= x.second)
++result;
}
}
}
}
/* for (int i = 1; i < n; ++i) {
for (int j = 1; j < m; ++j) {
cout << i << ' ' << j << ": " << endl;
cout << "HORIZONTAL: "; for (auto& x: horizontal_segments[i - 1][j]) cout << x.first << ' '; cout << endl;
cout << "VERTICAL: "; for (auto& x: vertical_segments[i][j - 1]) cout << x.first << ' '; cout << endl;
}
} */
return result;
}
